Sure, let's evaluate the given expression step by step for [tex]\(x = 4\)[/tex].
We need to evaluate the expression:
[tex]\[
\frac{3(x+4)(x+1)}{(x+2)(x-2)}
\][/tex]
for [tex]\(x = 4\)[/tex].
1. Substitute [tex]\(x = 4\)[/tex] into the expression:
[tex]\[
\frac{3(4+4)(4+1)}{(4+2)(4-2)}
\][/tex]
2. Simplify the terms inside the parentheses:
[tex]\[
\frac{3(8)(5)}{(6)(2)}
\][/tex]
3. Calculate the values inside the parentheses:
[tex]\[
\frac{3 \cdot 8 \cdot 5}{6 \cdot 2}
\][/tex]
4. Simplify the multiplication in the numerator and the denominator:
[tex]\[
\frac{120}{12}
\][/tex]
5. Finally, divide the numerator by the denominator:
[tex]\[
10
\][/tex]
So, the value of the expression [tex]\(\frac{3(x+4)(x+1)}{(x+2)(x-2)}\)[/tex] when [tex]\(x = 4\)[/tex] is [tex]\(\boxed{10}\)[/tex].
The correct answer is A. 10.
